Question

Each of the following equations was given by a student during an examination. Do a dimensional analysis of each equation and explain why the equation can't be correct.(a) 1/2 mv2 = 1/2mv02 + √mgh

Answer 1

The dimensional analysis of the given equation is solved as

`\begin{gathered} (1)/(2)mv^2=(1)/(2)mv^2_0+\sqrt[]{mgh} \\ \lbrack M^1L^2T^(-2)\rbrack=\lbrack ML^2T^(-2)\rbrack+\lbrack M^1L^2T^(-2)\rbrack^{(1)/(2)} \\ \lbrack M^1L^2T^(-2)\rbrack=\lbrack M^{(3)/(2)}L^3T^(-3)\rbrack \end{gathered}`

As the left-hand side of the dimension is not equal to the right-hand side of the dimension.

Hence, it is dimensionally incorrect.